Question

Compare Quantity A and Quantity B, using additional information centered above the two quantities if such information is given, and select one of the four answer choices: A symbol that appears more than once in a question has the same meaning throughout the question. \[ 10y + 20x = 50 \]

• A. Quantity A is greater
• B. The relationship cannot be determined from the information given
• C. The two quantities are equal
• D. Quantity B is greater

Hint:

When comparing quantities involving equations of lines, identify the key components (slope and y-intercept) and remember that without further information, their relationship may not be clear.

Answer 1

The Correct Option is B

Step 1: Analyze the equation.
We are given the equation \( 10y + 20x = 50 \). This is the equation of a line in the standard form. To find the y-intercept and slope, we will rewrite it in slope-intercept form \( y = mx + b \), where \( m \) is the slope and \( b \) is the y-intercept. \[ 10y = -20x + 50 \quad \Rightarrow \quad y = -2x + 5. \]
Step 2: Identify the quantities.
From the equation \( y = -2x + 5 \), we see that: \[ \text{Quantity A (y-intercept)} = 5, \quad \text{Quantity B (slope)} = -2. \]
Step 3: Conclusion.
The relationship between the y-intercept and the slope cannot be determined just from this equation without additional context. Thus, we cannot conclude a definitive comparison between the two quantities.